Optical systems: The eye, magnifier, microscope, telescope & binoculars

Optical systems:The eye, magnifier, microscope, telescope & binoculars Hecht 5.7 Monday October 7, 2002

Human Eye, Relaxed 20 mm 15 mm n’ = 1.33 F H H’ F’ 3.6 mm P = 66.7 D 7.2 mm

Accommodation • Refers to changes undergone by lens to enable imaging of closer objects • Power of lens must increase • There is a limit to such accommodation however and objects inside one’s “near point” cannot be imaged clearly • Near point of normal eye = 25 cm • Fully accommodated eye P = 70.7 for s = 25 cm, s’ = 2 cm

Myopia: Near Sightedness Eyeball too large ( or power of lens too large)

Myopia – Near Sightedness Far point of the eye is much less than ∞, e.g. lf Must move object closer to eye to obtain a clear image Normal N.P. Myopic F.P. Myopic N.P.

Myopia e.g. lf = 2m How will the near point be affected? 0.5 + 66.7 = 67.2 D is relaxed power of eye – too large! To move far point to ∞, must decrease power to 66.7 Use negative lens with P = -0.5 D

Laser Eye surgery Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball Usually use the 10.6 µm line of a CO2 laser for almost 100% absorption by the corneal tissue Blurred vision Front view

Laser Eye surgery Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball Usually use the 10.6 µm line of a CO2 laser for almost 100% absorption by the corneal tissue Distinct vision Front view Flattening

Hyperopia – Far Sightedness Eyeball too small – or lens of eye can’t fully accommodate Image of close objects formed behind retina

Hyperopia – Far Sightedness Suppose near point = 1m Recall that for a near point of 25 cm, we need 70.7D Use a positive lens with 3 D power to correct this person’s vision (e.g. to enable them to read) Usually means they can no longer see distant objects - Need bifocals

Correction lenses for myopia and hyperopia http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/V/Vision.html

Hand magnifier Observation with unaided eye θ

Magnifier To maximize the image, bring object as close to the eye as possible, i.e. bring object to near point s = ln = 25 cm h’ θmax

Hand Magnifier What is the angular magnification of the image for an object at the near point or at ∞? With thin lens H,H’ h” θ’ F so hM’ l f s’ L

Compound Microscope x’ L Fe Fo Fo Fe Recall xx’ = fo2 x x’ ≈ L Wish to have intermediate image (h’) just inside the focus of the eyepiece x = fo2/L s’ ≈ fo + L s = x + fo

Compound Microscope L Fe h h’ Fo Fo Fe h” • Recall: The magnification of an image formed • at the near point is • at infinity

Compound microscope Total magnification (Image at infinity) (Image at near point)

Compound Microscope In most microscopes, L ~ 16 - 17 cm Objective Eyepiece (image at ∞) 10 X, 20 X, 40 X etc fe = 2.5 cm 10X  Me = 10 40X  fo = 0.4 cm Overall magnification M = 40X10 = 400

Compound Microscope L A.S. Fe Fo Fo Fe EnP ExP Where should the eye be located to view the image? • Optimum viewing – • Place eye near ExP (moving eye away decreases illumination and F.O.V.) • Ensure that exit pupil ~ same size as eye pupil!

Compound Microscope L A.S. Fe Fo Fo Fe EnP ExP Chief Ray Marginal ray

Numerical Aperture Measure of light gathering power N. A. = n sin α Lens Air Oil αg αg’ αo αa Cover Glass ng O

Numerical Aperture If cover glass in air If cover glass immersed in oil (no = 1.516) – between glass and oil there is essentially no refraction since ng = 1.5 Increases the light gathering power by about 1.5 (N.A. roughly analogous to f# of a lens)

Numerical Aperture In optical fibres Cladding n2 Core n1 θc θ no αmax Cladding n2 N.A. = nosinαmax= n1sin θ = n1sin (90o - θc) = n1cos θc This is a measure of the maximum cone of light accepted

Viewing distant objects, e.g. stars star h θ feye Image size on retina h = feyeθ

Telescope Objective Eyepiece fo fe hT=feyeθ’ θ’ θ h’ θ’ h” s’

Telescope Show (magnification of the telescope) (diameter of the exit pupil)

The Hubble Space Telescope 0.3 m secondary mirror 2.4 m primary mirror

Binoculars Two telescopes side-by-side Prisms used to erect images Objective Eyepiece

Binoculars “6 X 30” Angular Magnification (M) Diameter of objective lens, Do (mm) Exit pupil = 5 mm, a good match to the normal pupil diameter For night viewing, a rating of 7 X 50 is better: i.e. ~ 7 mm

Optical systems: The eye, magnifier, microscope, telescope & binoculars